Gradient boosted trees are competition-winning, general-purpose, non-parametric regressors, which exploit sequential model fitting and gradient descent to minimize a specific loss function. The most popular implementations are tailored to univariate regression and classification tasks, precluding the possibility of capturing multivariate target cross-correlations and applying structured penalties to the predictions. In this paper, we present a computationally efficient algorithm for fitting multivariate boosted trees. We show that multivariate trees can outperform their univariate counterpart when the predictions are correlated. Furthermore, the algorithm allows to arbitrarily regularize the predictions, so that properties like smoothness, consistency and functional relations can be enforced. We present applications and numerical results related to forecasting and control.

We consider the problem of estimating the unobserved amount of photovoltaic (PV) generation and demand in a power distribution network starting from measurements of the aggregated power flow at the point of common coupling and local global horizontal irradiance (GHI). The estimation principle relies on modeling the PV generation as a function of the measured GHI, enabling the identification of PV production patterns in the aggregated power flow measurements. Four estimation algorithms are proposed: the first assumes that variability in the aggregated PV generation is given by variations of PV generation, the next two use a model of the demand to improve estimation performance, and the fourth assumes that, in a certain frequency range, the aggregated power flow is dominated by PV generation dynamics. These algorithms leverage irradiance transposition models to explore several azimuth/tilt configurations and explain PV generation patterns from multiple plants with nonuniform installation characteristics. Their estimation performance is compared and validated with measurements from a real-life setup including four houses with rooftop PV installations and battery systems for PV self-consumption.